Hemishpere

A hemishperical surface of radius R and refractive index mu = 1.5 is polished as shown. At what distance x from point P a point object O be placed so that its image coincides with the object itself?

A hemishperical surface of radius R and refractive index mu = 1.5 is polished as shown. At what distance x from point P a point object O be placed so that its image coincides with the object itself?

A circular disc of radius R is placed co-axically and horizontally inside an opaque hemishperical bowl of radius a as shown in Fig.6.02. . The far edge of the disc is just visible,when viewed from the edge of the bowl.The bols is filled with transparent liquid of refractive index mu and the near edge of the disc becomes just visible.How far below the top of the bowl is the disc placed?